Fuzzy Sets and Systems最新文献

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pseudo-FNN: Advancing fuzzy neural networks with pseudo-Unineurons and kernel density-based weights 伪神经网络（pseudo-FNN）：基于核密度权值的伪神经网络

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-22 DOI: 10.1016/j.fss.2026.109794

Paulo Vitor de Campos Souza

This study presents the pseudo-FNN, a fuzzy neural network model that integrates the pseudo-unineuron, a novel neuron type leveraging pseudo-uninorms to enhance non-commutative operations and knowledge extraction. The pseudo-FNN employs a three-layer architecture with Gaussian fuzzy neurons, where weights are derived from kernel density estimation and rule consequents are optimized using multiple algorithms. Experimental evaluations on four datasets (Iris, Haberman, Transfusion, and Mammographic Masses) demonstrate the model’s competitive performance. The pseudo-FNN outperformed traditional fuzzy neural networks such as ANFIS and showed comparable results with optimization-enhanced FNNs. Among the optimization techniques, models using SGD, Adam, and RMSProp achieved the most consistent and high accuracies across datasets with pseudo-FNN models often aligning with these trends. Statistical analysis confirmed significant improvements over non-optimized models, and the pseudo-FNN demonstrated robustness in addressing varying classification complexities. These results highlight the effectiveness of the pseudo-unineuron in advancing fuzzy neural network architectures.

本文提出了一种融合了伪统一神经元（pseudo-unineuron）的模糊神经网络模型——伪统一神经元（pseudo-unineuron），这是一种利用伪统一信息来增强非交换运算和知识提取的新型神经元类型。伪fnn采用高斯模糊神经元的三层结构，其中权值来自核密度估计，规则结果使用多种算法进行优化。在四个数据集（虹膜、哈伯曼、输血和乳房x线图像质量）上的实验评估证明了该模型的竞争性表现。伪模糊神经网络的性能优于传统模糊神经网络（如ANFIS），并显示出与优化增强模糊神经网络相当的结果。在优化技术中，使用SGD、Adam和RMSProp的模型在数据集上实现了最一致和高精度，而伪fnn模型通常与这些趋势保持一致。统计分析证实了非优化模型的显著改进，并且伪fnn在处理不同的分类复杂性方面表现出鲁棒性。这些结果突出了伪神经元在推进模糊神经网络结构方面的有效性。

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引用次数: 0

Regular orders for triangular fuzzy numbers and the weak law of trichotomy 三角模糊数的正则阶数及弱三分律

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-22 DOI: 10.1016/j.fss.2026.109790

Jaime Cesar dos Santos

Building upon specific compatibility conditions, we establish fundamental structural results concerning ordering relations for triangular fuzzy numbers. We demonstrate that orders satisfying compatibility with arithmetic operations, MIN-MAX operators, and the Weak Law of Trichotomy (WLT) are completely determined on the fibers of the natural projection to real numbers. Furthermore, such orders naturally induce — in analogy with real numbers — well-defined notions of fuzzy absolute value and fuzzy distance that preserve the essential properties of their classical counterparts. These results enable us to characterize open and closed balls through interval representations, providing a robust theoretical framework for future studies regarding metric properties of fuzzy numbers.

在特定相容条件的基础上，我们建立了关于三角模糊数序关系的基本结构结果。证明了在实数自然投影的纤维上，满足算术运算、最小-最大算子和弱三分法（WLT）相容的阶数是完全确定的。此外，与实数类似，这样的数列自然会引出模糊绝对值和模糊距离的定义良好的概念，这些概念保留了经典数列的基本属性。这些结果使我们能够通过区间表示来表征开放球和封闭球，为未来关于模糊数度量性质的研究提供了一个强大的理论框架。

引用次数: 0

Characterizations and relation of generalized differentiabilities of interval-valued functions and fuzzy number-valued functions 区间值函数和模糊值函数的广义可微性的刻画及其关系

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-20 DOI: 10.1016/j.fss.2026.109789

Dong Qiu , Nianxi Huang , Yandan Jiang

In this paper, by using the properties of their endpoint-valued functions, we gave characterizations of various generalized differentiabilities of interval-valued functions and fuzzy number-valued functions, which provide more convenient calculating and discriminating formulas than directly according to the definitions. By comparing these characterizations, we revealed the complete and detailed connection between the different types of differentiabilities. In addition, for n-fold interval-valued functions, we proposed two new definitions: combined gH-differentiability of coordinate components and metric-based differentiability in coordinates, to generalize existing differentiabilities; for fuzzy number-valued functions, we introduced gH^⁎⁎-differentiability to improve the existing gH*-differentiability. The obtained results extend and improve the ones in the literature.

本文利用区间值函数和模糊值函数的端点值函数的性质，给出了区间值函数和模糊值函数的各种广义可微性的刻画，提供了比直接根据定义更方便的计算和判别公式。通过比较这些表征，我们揭示了不同类型的可微性之间完整而详细的联系。此外，对于n重区间值函数，我们提出了两个新的定义：结合坐标分量的h -可微性和坐标上基于度量的可微性，以推广现有的可微性；对于模糊数值函数，我们引入了gH*-可微性，改进了已有的gH*-可微性。所得结果扩展和改进了文献中的结果。

引用次数: 0

A topological approach to fuzzy iterated function systems 模糊迭代函数系统的拓扑方法

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-20 DOI: 10.1016/j.fss.2026.109791

Taras Banakh , Krzysztof Caban , Filip Strobin

In the paper we unify two extensions of the classical Hutchinson–Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuzzy IFS) on a Tychonoff space X which is contracting w.r.t. some admissible multimetric, generates a natural fuzzy attractor in the hyperspace

K_{F} (X)

of all compact fuzzy sets. As a consequence, we prove that a fuzzy IFS on a Hausdorff topological space which is topologically contracting admits a fuzzy attractor in a bit weaker sense. Our discussion involves investigations on topologies on the hyperspace

K_{F} (X)

which are suitable for establishing convergence of sequences of iterations of a fuzzy Hutchinson operator.

本文统一了经典Hutchinson-Barnsley理论的两个扩展——拓扑方法和模糊集方法。我们证明了Tychonoff空间X上的模糊迭代函数系统（fuzzy IFS）在所有紧模糊集的超空间KF(X)上产生一个自然模糊吸引子。因此，我们证明了拓扑收缩的Hausdorff拓扑空间上的模糊IFS存在较弱意义上的模糊吸引子。我们的讨论涉及对超空间KF(X)上的拓扑的研究，这些拓扑适合于建立模糊Hutchinson算子迭代序列的收敛性。

引用次数: 0

Ω-vector spaces Ω向量空间

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-16 DOI: 10.1016/j.fss.2026.109776

Patricia Ferrero , Jorge Jiménez , María Luisa Serrano , Branimir Šešelja , Andreja Tepavčević

In this work, we introduce the concept of Ω-vector spaces, extending the framework of Ω-algebras by incorporating a vector space structure over a field. These structures are defined over a complete lattice and equipped with an Ω-valued equality, which replaces the classical relation of being equal. We provide an equivalent characterization of Ω-vector spaces via cut-quotient structures and prove that each cut induces a classical vector space. Furthermore, we introduce the notion of Ω-vector subspaces and investigate the lattice-theoretic properties of their collection, including intersections and sums. Finally, we show an application for approximately solving systems of linear equations in this context. Several examples illustrate the theory, highlighting the algebraic richness and structural consistency of Ω-vector spaces.

在这项工作中，我们引入了Ω-vector空间的概念，通过在场上加入向量空间结构来扩展Ω-algebras的框架。这些结构被定义在一个完全晶格上，并配备了一个Ω-valued等式，它取代了经典的相等关系。我们通过切商结构给出了Ω-vector空间的等价表征，并证明了每个切都可以导出一个经典向量空间。进一步，我们引入了Ω-vector子空间的概念，并研究了它们集合的格论性质，包括交集和。最后，我们给出了近似求解线性方程组的一个应用。几个例子说明了这一理论，突出了Ω-vector空间的代数丰富性和结构一致性。

引用次数: 0

Distributivity between S-uninorms and general overlap or general grouping functions s -一致函数与一般重叠或一般分组函数之间的分布性

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-16 DOI: 10.1016/j.fss.2026.109777

Jieqiong Shi , Bin Zhao , Bernard De Baets

It is well known that the distributivity of one aggregation function over another is a desirable interaction between aggregation functions and has been continuously studied in the literature both for theoretical and practical reasons. Among the many classes of aggregation functions introduced over the past decades, the classes of uninorms and nullnorms stand out because of their potential applications in a broad variety of fields. Similarly, the classes of overlap and grouping functions have received ample attention. In this paper, on the one hand, we focus on the class of S-uninorms, a common generalization of nullnorms and conjunctive uninorms. On the other hand, we consider other more general classes of general overlap and general grouping functions. We continue and wrap up the investigation of the distributivity equation for the above-mentioned classes. In particular, we discuss the distributivity of S-uninorms (with an underlying uninorm belonging to

U_{\min}

) over general overlap or general grouping functions, and vice versa. In both cases, we fully characterize the solutions by providing necessary and sufficient conditions.

众所周知，一个聚集函数对另一个聚集函数的分布性是聚集函数之间理想的相互作用，由于理论和实践的原因，文献中不断地对其进行研究。在过去几十年中引入的许多类聚合函数中，一致范数和零范数类因其在各种领域的潜在应用而脱颖而出。同样，重叠函数类和分组函数类也得到了充分的关注。在这篇论文中，我们一方面关注了s -一致子的范畴，它是零范数和合一致子的一般推广。另一方面，我们考虑其他更一般的类的一般重叠和一般分组函数。我们继续并结束对上述类的分配方程的研究。特别地，我们讨论了一般重叠函数或一般分组函数上s -一致子（其底层一致子属于Umin）的分布性，反之亦然。在这两种情况下，我们通过提供必要和充分条件来充分表征解。

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引用次数: 0

Practically predefined-time adaptive fuzzy control for stochastic nonlinear systems with full state constraints and dead zones 具有全状态约束和死区随机非线性系统的实际预定义时间自适应模糊控制

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-15 DOI: 10.1016/j.fss.2026.109779

Mengqing Cheng , Shuo Shan , Junsheng Zhao , Shixiong Fang , Haikun Wei , Kanjian Zhang

This paper investigates a dynamic event-triggered practically predefined-time control (PPTC) scheme for stochastic nonlinear systems (SNSs) under state constraints and input dead zones. A nonlinear state-dependent function (NSDF) is introduced to enforce state constraints. To address input dead-zone nonlinearities and mitigate the complexity growth inherent in backstepping, novel predefined-time compensating filters (PTCFs) and predefined-time filters (PTFs) are designed. These filters guarantee the convergence of filter states within a predefined time and effectively suppress the influence of dead zones. Building on this, a semiglobal predefined-time adaptive fuzzy tracking control algorithm is developed, where a fuzzy logic system (FLS) approximates unknown nonlinear dynamics. Furthermore, a dynamic event-triggered mechanism (DETM) is incorporated into the framework to reduce communication load. The present control scheme ensures tracking error convergence within a predefined time and uniform boundedness of all closed-loop signals in the pth moment. Finally, a simulation example is conducted to demonstrate the effectiveness of the proposed strategy.

研究了随机非线性系统在状态约束和输入死区条件下的动态事件触发实际预定义时间控制（PPTC）方案。引入非线性状态相关函数（NSDF）来加强状态约束。为了解决输入死区非线性问题并减轻反推过程中固有的复杂性增长，设计了新型的预定义时间补偿滤波器（ptcf）和预定义时间滤波器（PTFs）。这些滤波器保证了滤波器状态在预定义时间内的收敛性，并有效地抑制了死区的影响。在此基础上，提出了一种半全局预定义时间自适应模糊跟踪控制算法，其中模糊逻辑系统（FLS）逼近未知非线性动力学。此外，该框架还引入了动态事件触发机制（DETM），以减少通信负荷。该控制方案保证了跟踪误差在预定时间内收敛，并保证了所有闭环信号在第pth时刻的均匀有界性。最后，通过仿真实例验证了所提策略的有效性。

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引用次数: 0

On the coincidence of the Choquet integral and the pan-integral: An abstract setting and examples 关于Choquet积分与泛积分的重合：一个抽象的背景和例子

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-14 DOI: 10.1016/j.fss.2026.109774

M. Svistula, T. Sribnaya, R. Uzbekov

In the present paper we propose such an abstract setting, which allows us to obtain as consequences both known and new results on the coincidence of the Choquet integral and the pan-integral. For example: in the case of a measurable space we derive a well-known theorem that the weak (M)-property of a monotone measure is necessary and sufficient for the coincidence of the integrals under consideration for all nonnegative measurable integrands; in the case of a topological space we use the integrals with respect to a regular monotone measure and establish some new results, in particular, that the Choquet integral and the pan-integral with respect to a topological measure coincide for all nonnegative lower semicontinuous integrands.

Next, in the case of a measurable space we give an example to show that the weak (M)-property is weaker than the middle (M)-property, and thus we solve an open problem of the relationship between these properties.

在本文中，我们提出了这样一个抽象的设定，它使我们可以得到关于Choquet积分与泛积分重合的已知结果和新的结果。例如：在可测空间中，我们导出了一个众所周知的定理，即单调测度的弱(M)-性质对于所考虑的所有非负可测积分的一致性是充分必要的；在拓扑空间中，我们利用关于正则单调测度的积分，建立了一些新的结果，特别是对于所有非负下半连续积分，关于拓扑测度的Choquet积分与泛积分重合。其次，在可测空间中，我们给出了弱(M)-性质比中(M)-性质弱的例子，从而解决了这些性质之间关系的一个开放问题。

引用次数: 0

Solving fuzzy linear systems in Gaussian PDMF space 求解高斯PDMF空间中的模糊线性系统

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-14 DOI: 10.1016/j.fss.2026.109772

Chuang Zheng

<div><div>In this paper, we solve the fuzzy linear systems in a fuzzy number space <span><math><mi>X</mi></math></span>, namely the Gaussian probability density membership function (Gaussian-PDMF) space. The fuzzy linear systems include two types: the semi-fuzzy linear system (SFLS) and the fully-fuzzy linear system (FFLS). First, we solve the SFLS <span><math><mrow><mi>A</mi><mrow><mover><mi>x</mi><mo>˜</mo></mover></mrow><mo>=</mo><mrow><mover><mi>b</mi><mo>˜</mo></mover></mrow></mrow></math></span>, where <span><math><mrow><mi>A</mi><mo>∈</mo><msup><mi>R</mi><mrow><mi>m</mi><mo>×</mo><mi>n</mi></mrow></msup></mrow></math></span> is a real-valued matrix, <span><math><mrow><mover><mi>b</mi><mo>˜</mo></mover></mrow></math></span> is a fuzzy number vector, and <span><math><mrow><mover><mi>x</mi><mo>˜</mo></mover></mrow></math></span> is the unknown fuzzy number vector. The elements of both <span><math><mrow><mover><mi>b</mi><mo>˜</mo></mover></mrow></math></span> and <span><math><mrow><mover><mi>x</mi><mo>˜</mo></mover></mrow></math></span> belong to <span><math><mi>X</mi></math></span>. We present the Cramer’s rule to calculate the solution with square matrix <em>A</em> and find out that its solution set is a <span><math><mrow><mn>5</mn><mo>(</mo><mi>n</mi><mo>−</mo><mi>R</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo></mrow></math></span> dimensional affine space with <span><math><mrow><mi>A</mi><mo>∈</mo><msup><mi>R</mi><mrow><mi>m</mi><mo>×</mo><mi>n</mi></mrow></msup></mrow></math></span> and <em>R</em>(<em>A</em>) being the rank of <em>A</em>. The explicit form of the solution for RREF matrix <em>A</em> is stated to ensure usability for modeling. Secondly, we solve the FFLS <span><math><mrow><mrow><mover><mi>A</mi><mo>˜</mo></mover></mrow><mrow><mover><mi>x</mi><mo>˜</mo></mover></mrow><mo>=</mo><mrow><mover><mi>b</mi><mo>˜</mo></mover></mrow></mrow></math></span>, where <span><math><mrow><mover><mi>A</mi><mo>˜</mo></mover></mrow></math></span> is a fuzzy matrix with all components in <span><math><mi>X</mi></math></span>. We analyze its solution set and present the parametric form of solutions under the fuzzy RREF matrix. We then adapt Gaussian elimination method to fuzzy matrices and systems by restricting it to the unit group of ring <span><math><mi>X</mi></math></span>, proving the equivalence of solution sets after elementary row operations. We also establish the connection between FFLS and SFLS by confining elements of <span><math><mrow><mover><mi>A</mi><mo>˜</mo></mover></mrow></math></span> to a subset of <span><math><mi>X</mi></math></span> that forms a field. In the third part, two numerical examples are given to illustrated our method. All results in this paper are explicit since the Gaussian-PDMF space <span><math><mi>X</mi></math></span>, to which the membership function of the fuzzy number belongs, possesses a complete algebraic structure. The proposed framework offers a feasible and systematical tool for solving the mathematical m

本文在模糊数空间X，即高斯概率密度隶属函数（Gaussian- pdmf）空间中求解模糊线性系统。模糊线性系统包括半模糊线性系统和全模糊线性系统两种类型。首先，我们求解SFLS Ax ~ =b ~，其中A∈Rm×n为实值矩阵，b ~为模糊数向量，x ~为未知模糊数向量。我们提出了计算具有方阵A的解的Cramer规则，并发现其解集是一个5（n−R(A)）维仿射空间，其中A∈Rm×n， R(A)为A的秩。为了保证建模的可用性，我们给出了RREF矩阵A解的显式形式。其次，我们求解了FFLS A ~ x ~ =b ~，其中A ~是一个所有成分都在x中的模糊矩阵，我们分析了它的解集，并给出了模糊RREF矩阵下解的参数形式。然后将高斯消去法限定在环X的单位群上，将其应用于模糊矩阵和系统，证明了初等行运算后解集的等价性。我们还通过将A ~的元素限定为X的一个子集来建立FFLS和SFLS之间的联系。在第三部分中，给出了两个数值例子来说明我们的方法。由于模糊数的隶属函数所在的高斯- pdmf空间X具有完备的代数结构，所以本文的所有结果都是显式的。该框架为求解具有不确定性和模糊性的模糊线性系统的数学模型提供了一种可行的系统工具。

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引用次数: 0

Adaptive dynamic event-triggered control for IT-2 fuzzy delayed semi-Markov jump systems with different uncertain transition rates 具有不同不确定过渡速率的IT-2模糊延迟半马尔可夫跳变系统的自适应动态事件触发控制

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-01-14 DOI: 10.1016/j.fss.2026.109773

Hao Qiu , Huamin Wang , Likui Wang , Shiping Wen

In practical industrial systems, we often encounter nonlinear uncertainties, parameter jumps, or time-delay phenomena that easily destroy the stability of the system. To stabilize these disturbances, we construct a more general closed-loop interval type-2 fuzzy delayed semi-Markov jump system (IT-2FD S-MJS) and investigate its stochastic stability in this article. Firstly, to optimize the performance of computational resources and data transmission, we introduce quantization techniques and novel adaptive dynamic data sampling-based event-triggered mechanisms, greatly reducing the number of triggers and improving the flexibility of adjustment. The framework’s discrete sampling nature inherently prevents Zeno behavior by eliminating the possibility of infinite triggers within finite time intervals. Then, by constructing boundary/general uncertain transition rates (BUTR/GUTR) and slack matrices, we derive sufficient conditions with less conservatism of stochastic stability for IT-2FD S-MJS. It should be noticed that the unknown transition information is modeled by BUTR/GUTR, and the conservatism of mismatched membership functions is reduced by introducing the slack matrices. Meanwhile, we obtain the corresponding gain parameters of the adaptive dynamic event-triggered quantization controller using linear matrix inequality (LMI) technology, with implementation details specified in Algorithms 1 and 2. Finally, we take the robotic arm and tunnel diode circuit as examples to verify the validity of the theorems.

在实际的工业系统中，我们经常会遇到非线性不确定性、参数跳跃或时滞现象，这些现象很容易破坏系统的稳定性。为了稳定这些扰动，我们构造了一个更一般的闭环区间2型模糊延迟半马尔可夫跳变系统（IT-2FD - S-MJS），并研究了它的随机稳定性。首先，为了优化计算资源和数据传输性能，我们引入了量化技术和基于自适应动态数据采样的事件触发机制，大大减少了触发次数，提高了调整的灵活性。该框架的离散采样特性固有地通过消除有限时间间隔内无限触发器的可能性来防止芝诺行为。然后，通过构造边界/一般不确定过渡率（BUTR/GUTR）和松弛矩阵，得到了IT-2FD S-MJS随机稳定性保守性较低的充分条件。需要注意的是，未知的过渡信息是用BUTR/GUTR建模的，并且通过引入松弛矩阵来降低不匹配隶属函数的保守性。同时，我们利用线性矩阵不等式（LMI）技术获得了自适应动态事件触发量化控制器的相应增益参数，具体实现方法见算法1和算法2。最后，以机械臂和隧道二极管电路为例验证了定理的有效性。

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